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If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Home » math » Evaluating Expressions: Definition, Solved Examples Evaluating Expressions: Definition, Solved Examples Evaluating Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator In mathematics, algebraic expressions are constructed upon constants and variables. They are also made up of algebraic operations such as addition, subtraction, etc. Sometimes, these expressions can be seen in terms as well. Once we define these expressions, we have to evaluate them. Evaluating an expression includes finding a missing variable. This is by replacing it with a given number. Moreover, it does not just stop over there. One needs to translate and simplify these sentences as well. All these concepts, including how to evaluate expressions with a deep understanding of subtopics, will be explained below. How to Evaluate ExpressionsWhat does “evaluate the expression” mean? Simplification of expressions can be done with the help of operations’ order. The following passage is about evaluating expressions. It includes replacing the variable to find the expression’s value. The given number is substituted to evaluate expressions. After this, one needs to simplify it based on the order of the operations. This is how we evaluate each expression. Let us look at an example: Example 1: Evaluate y + 12 when
Solution:
=y + 12 =15 + 12 = 27 Hence, the value of y is 27.
=y + 12 =3 + 12 = 15 Hence, the value of y is 15. From the example, it is seen that it is possible to obtain various results for the same expression. It is because y had different values. So, from this, one can understand that the results completely rely on the value of the variable. Let us look at more examples and understand how to evaluate expression Example 2: Evaluate expression: x + 3
Solution:
= x + 3 = 6 + 3 = 9 Hence, the value of x is 9.
= 9 + 3 = 9+3 = 12 Hence, the value of x is 12. Let’s see some more complex examples, where we evaluate each expression: Example 3: Evaluate expression: 2 z + 3, when
Solution: To evaluate, one needs to keep in mind that 2 z means 2 times the value of z.
2 z + 3 = 2 (2) + 3 = 4 + 3 = 7 Hence, the value of z is 7.
2 z + 3 = 2 (5) + 3 = 10 + 3 = 13 Hence, the value of z is 13. Example 4: Evaluate expression: y2 when y = 3 Solution: Substituting 3 for y in the given expression: y2 = 32 = 3 * 3 = 9 Hence, the value of y2 is 9, while substituting y = 3. Example 5: Evaluate expression: 3Z when z = 4. Solution: Substituting 4 for z in the given expression: =3Z = 34 = 3 * 3 * 3 * 3 = 81 Hence, the value of 3Z is 81, while substituting z = 4. Example 6: Evaluate expression: 7 x + 5 y – 2 when x = 5 and y = 4 Solution: This example consists two variable, to evaluate this expression, one should substitute both the values. As this expression consists of two variables, one should substitute both the values. Substituting 5 for x and 4 for y in the given expression, = 7 x + 5 y – 2 = 7 (5) + 5 (4) -2 = 35 + 20 -2 = 53 Hence, the value of the expression 7 x + 5 y – 2 is 53. Lastly, let us see an example with an expression that contains a variable with an exponent. Example 7: Evaluate expression: 2 y2 + 3 y + 4 when y = 2 Solution: The expression needs to be solved carefully. It is because the variable in it contains an exponent. In the expression, 2 y2 indicates 2 * y * y. It is different from the expression, (2 y)2, which denotes 2 y * 2 y. Substitute 2 for each y in the given expression, = 2 y2 + 3 y + 4 = 2 (2)2 + 3 (2) + 4 = 8 + 6 + 4 = 18 Hence, the value of the expression 2 y2 + 3 y + 4 when y = 2 is 18. Identifying terms, coefficients, and like termsThese expressions are also made up of terms. A term can be denoted as a constant. In other cases, terms can be products of constants and one or more variables. Examples of terms are 5, 6 x, y2, 12 x y, etc. A coefficient is nothing but a constant that multiplies the variable. They are present in front of the variables. For example, in the term 4 y, the coefficient here is 4. But in the term x, the coefficient here is 1. Let us have a look at the following to know about terms and coefficients even better: TermCoefficient 14 x1425 z2251212a21x1Algebraic Expressions: Algebraic Expressions are used to calculate solutions for any Mathematical operations that include variables such as addition, subtraction, multiplication or division. There are three types of algebraic expressions; Monomial Expression, Binomial Expression, and Polynomial Expression. An unknown value is represented as the letters x,y and z in the fundamentals of Algebraic expressions. These letters are referred to as variables. An algebraic expression can have both variables and constants. Together they form the algebraic expression. Algebraic expressions are constructed up on one or more terms. For example: Expression Terms99zzy + 9y, 95 x + 6 y + 165 x, 6 y, 166 z4 + 9 y + 14 x2 + 12 y 36 z4, 9 y, 14 x2, 12 y, 32 x2 + 7 y2 + 2 x y + 92 x2, 7 y2, 2 xy, 9Here are a few more examples:Example 8: Determine all the terms in the given expression. 14 a2 + 2 b + 6 x y + 3. Also, find the coefficient of each term. Solution: The given expression consists of four terms in it. They are 14 a2 , 2 b, 6 x y, and 3. The coefficient of 14 a2 is 14. The coefficient of 2 b is 2. The coefficient of 6 x y is 6. Finally, 3 is already a coefficient, since it is a constant. Example 9: Determine all the terms and their coefficients in the given expression: a3 + 9 y5 + 6 x2 + 4. Solution: The given expression has four terms in it. They are a3, 9 y5, 6 x2, 4. The coefficients are 1, 9, 6, and 4. Moreover, there are certain terms in an expression that could share common traits. For example: 4 y, 8, m2, 2, 3 y, 6 m2 The following are the like terms for the given example:
From this, one can easily understand that if two or more terms have the same variables and exponents, then they are said to be like terms. In addition to this, all constant terms are like terms. So, due to this reason: 4 y and 3 y are like terms. m2 and 6 m2 are like terms. 8 and 2 are like terms. Looking at the following example: Example 10: Determine the like terms: x2 + 4 y + 8 z3 + 7 + z3 + 2 y + 7 x2 + 3 + 12 x Solution: While looking for similar terms, one needs to focus on the variables and exponents. The expression has x2 terms, y terms, z3 terms, and constant terms. The terms x2 and 7 x2 are like terms. This is because they both have x2 in them. The terms 4 y and 2 y are like terms. This is because they both have y in them. The terms 8 z3 and z3 are like terms. This is because they both have z3 in them. The terms 7 and 3 are constants. So they are also like terms. Lastly, the term 12 x does not have a similar term. So it is not a like term. Simplifying expressions by combining like termsThis is a very simple concept. It just means adding the like terms together and forming a whole new term, which is a combination of both. For example, let’s take the expression, 3 z + 4 z. As discussed earlier, we just need to add both the coefficients and keep the variable as it is. It becomes, 3 z + 4 z = 7 z, which means 7 times the value of z. Let us have a look at another example: 6 y + 7 z – 4 y + z. This expression becomes, 6 y – 4y + 7 z + z. It gives, 2 y + 8 z. From this learners can easily understand that the expression becomes easier by:
ConclusionExpressions are the most commonly used items in mathematics. One needs to understand how to evaluate expressions to simplify the problems easily. What does it mean to evaluate an expression? All the students learning this chapter should have a detailed idea of that. In addition to this, it is essential to understand what does evaluate the expression means. Everything mentioned above was deeply discussed in this chapter. TESTIMONIALSAyaan always had a special interest in Math. His knowledge and problem solving skills in math has been improving after enrolling in Turito's One-on-One onlineTutoring. The tutors are very co-operative and the valuable tips given by them made his learning more enjoyable.They were also very interactive and my son is able to communicate better than ever before. The best thing about Turito’s one-on-one tutoring is the flexible timings and the tutors are at our reach anytime, anywhere. This actually made my son’s learning seamless and saved a lot of time. Parent: Dr.Sadaf asad | Subject : Math I witnessed a significant improvement in the English language skills of my son Trijal, after enrolling in Turito’s one-on-one tutoring. The sessions were undoubtedly interesting. Though Trijal is shy by nature, now he is able to interact smoothly because the tutors established a friendly rappo with him. Parent: Kamal Narang | Subject : English My daughter, Karmanpreet’s English grammar, Reading and spelling skills have tremendously improved after enrolling in Turito's One-On-One Tutoring. Their services are flexible, and the tutors are very co-operative. She looks forward to these sessions as they include fun activities and make learning quite enjoyable and stress-free. Parent: Gurpreeth Sandhu | Subject : English Previous Next SIGNUP FOR AFREE SESSION
First Name Last name Country Mobile Your email Grade More RelatedTOPICSA composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of Special Right Triangles: Types, Formulas, with Solved Examples.Learn all about special right triangles- their types, formulas, and examples explained in detail for a Ways to Simplify Algebraic ExpressionsSimplify algebraic expressions in Mathematics is a collection of various numeric expressions that multiple philosophers and How do you evaluate an equation?To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.
Whats does evaluate mean in math?To determine or calculate the value of.
What does it mean to evaluate a formula?The Evaluate Formula feature walks you through each argument in a formula to help identify and fix any mistakes. You can also use it to understand complex formulas, seeing how each part of a nested function is calculated to reach the final result.
What is an example of evaluate in math?To calculate the value of. Example: Evaluate the cost of each pie when 3 pies cost $6. Answer: $2 each.
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